The most common and most likely answer to this crossword clue is the 8 letter word VESTMENT
I've seen this crossword clue in The Daily Telegraph
V
E
S
T
M
E
N
T
More clues leading to the result VESTMENT
Buddy explains!

The straight part
We know that "Outfit" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case outfit = vestment.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does VESTMENT mean?
VESTMENT noun- A robe, gown, or other article of clothing worn as an indication of office.
- Any of the special articles of clothing worn by members of the clergy etc., especially a garment worn at the celebration of the Eucharist.
- (in plural) Clothing.
- An article of clothing, especially an outer garment.